Let \(\lbrace p_t\rbrace _{t>0}\)  be an \(m\) -symmetric Markovian transition function of \({\mathbf {M}}\) 
on \((X,{\cal B}(X))\) .
Then it uniquely associates an strongly continuous Markovian semigroup \(\lbrace T_t\rbrace _{t>0}\) 
and thus a Dirichlet form \(({\cal E},{\cal F})\)  on \(L^2(X;m)\)  ([1]}).
The next theorem shows a probabilistic consequence of the recurrence of irreducible Dirichlet forms.
